Gujarat Board Statistics Class 11 GSEB Solutions Chapter 4 Measures of Dispersion Ex 4.5 Textbook Exercise Questions and Answers.
Gujarat Board Textbook Solutions Class 11 Statistics Chapter 4 Measures of Dispersion Ex 4.5
Question 1.
Price fluctuations of two shares A and B are given below, which type of share has more relative variation in its price?
Answer:
To determine which share price has more relative variation, we calculate coefficient of variation of prices of share A and share B.
Share A
Mean:
x̄ = \(\frac{\Sigma x}{n}=\frac{3210}{10}\) = ₹ 321
Standard deviation:
s = \(\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{n}}\)
= \(\sqrt{\frac{70}{10}}\)
= √7
= ₹ 2.65
Coefficient of variation:
Variation = \(\frac{s}{\bar{x}}\) × 100
= \(\frac{2.65}{321}\) × 100
= 0.0083 × 100
= 0.83%
Share B
Mean:
x̄ = \(\frac{\Sigma x}{n}=\frac{1400}{10}\) = ₹ 140
Standard deviation:
s = \(\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{n}}\)
= \(\sqrt{\frac{510}{10}}\)
= √51
= ₹ 7.14
Coefficient of variation:
Variation = \(\frac{s}{\bar{x}}\) × 100
= \(\frac{7.14}{140}\) × 100
= 0.051 × 100
= 5.1%
Coefficient of variation of price of share A 0.83% and that of share B it is 5.1%. Hence, the relative measure of variation is more in the price of share B.
Question 2.
The daily salary of administrative staff of two companies yielded the following results:
| Company A | Company B | |
| Mean salary(₹) | 600 | 2100 |
| Standard Deviation (₹) | 30 | 84 |
Which company has more stable salary?
Answer:
Company A
x̄ = ₹ 600
s = ₹ 30
Coefficient of variation = \(\frac{s}{\bar{x}}\) × 100
= \(\frac{30}{600}\) × 100
= 5%
Company B:
x̄ = ₹ 2100
s = ₹ 84
Coefficient of variation = \(\frac{s}{\bar{x}}\) × 100
= \(\frac{84}{2100}\) × 100
= 4%
The coefficient of variation of daily salary of employees of company A is 5 % and that of company B it is 4 %. Hence, the daily salary in company B Is more stable.
Question 3.
The Coefficients of variation of two series are 30% and 25% and their standard deviations are 15 and 9 respectIvely. Find their means.
Answer:
First Series:
Coefficient of variation: 30%
s = 15
x̄ = ?
Coefficient of variation = \(\frac{s}{\bar{x}}\) × 100
∴ 30 = \(\frac{15}{\bar{x}}\) × 100
∴ 30x̄ = 1500
∴ x̄ = \(\frac{1500}{30}\)
∴x̄ = 50
Second series:
Coefficient of variation: 25%
s = 9
x̄ = ?
Coefficient of variation = \(\frac{s}{\bar{x}}\) × 100
∴ 25 = \(\frac{9}{\bar{x}}\) × 100
∴ 25x̄ = 900
∴ x̄ = \(\frac{900}{25}\)
∴x̄ = 36